Democrats in Wisconsin chose Tom Barrett, mayor of Milwaukee, to challenge Gov. Scott Walker (R) in a recall election next month. It's a reprise of their 2010 contest, but now Walker has a record to defend.

The first time, Mr. Walker won by almost six percentage points. But the governor now faces a recall election, and this time he has a record to defend. That means this new election – set for June 5 – will be quite a bit different from the last, say some political analysts.

“Scott Walker now has a record and Barrett will want to attack that record. The dynamic is really different when you have an incumbent running,” says John McAdams, a political scientist at Marquette University in Milwaukee.

Walker’s campaign took little time to point out that Barrett is entering his “third statewide losing campaign” for governor, according to a statement released late Tuesday. Barrett also ran for governor in 2002 but lost in his party’s primary.

The top issue facing both candidates is jobs. Nearly half of primary voters rank “creating new jobs” as the most important issue in the race, while 25 percent say they are voting simply to defeat Walker, according to early May polling by the Marquette University School of Law. Twelve percent said the prevailing issue is restoring the collective bargaining rights of public-sector employees. Last year, Walker pushed through legislation that curtailed those rights, igniting a firestorm that carried through to the current recall. [Editor's note:The original version has been changed to correct the name of the law school that did the polling.]

Although Wisconsin’s unemployment rate is the lowest it has been since 2008, only 5,900 private-sector jobs have been created since Walker took office. (He had pledged during his first campaign that there would be 250,000 new jobs during his four-year term, which is now halfway over.] Moreover, the state lost more jobs than any other between March 2011 and March 2012, according to the US Bureau of Labor Statistics.

Barrett is expected to seize on that data to reinforce his message that Walker’s agenda hurts job growth.

Speaking to supporters Tuesday in Milwaukee, Barrett said the governor will “run from that record.”

“He took the eye off the ball. Instead of doing what he said he was going to do, which was to create 250,000 jobs, he looked for new way to divide us from each other,” Barrett said.

Walker is attacking Barrett, too, on the jobs issue, saying Milwaukee’s unemployment rate rose 28 percent over the past eight years even as property taxes in the city jumped 25 percent. He is championing his bid to curb collective bargaining rights, saying it helped to save state taxpayers $1 billion and prevented a tax increase during his first year in office.

Walker did not mention Barrett by name late Tuesday in remarks to supporters in Waukesha, Wis. “The powerful special interests don't like the fact that I stood up and got in the way of their firm grip on the taxpayers' money. Instead, I stand with the taxpayers of this state,” he said.

Barrett has been the presumptive nominee for weeks, after polls showed him more likely to give Walker a tight race than Kathleen Falk, the former Dane County executive and his closest competitor.

As mayor, Barrett has often had a contentious relationship with labor unions. Their support in the primary largely went to Ms. Falk. The two candidates differed on how they would restore collective bargaining rights – Falk said she would veto any state budget that didn’t restore them, while Barrett said it would be more appropriate to hold a special session to vote on the issue.

With Barrett as the Democratic nominee, labor unions are expected to shift their support to his campaign, says Georgia Duerst-Lahti, a political scientist at Beloit College in Beloit, Wis.

“In the end, the unions want Walker gone,” says Ms. Duerst-Lahti. “There is a lot of voter remorse among independents and moderate, conservative Democrats who voted for Walker last time, but we’re not in that spot anymore.”

Although Barrett polled better against Walker than Falk did, the recall race is expected to be tight. According to Marquette’s polling, Walker leads Barrett by one percentage point among likely voters.

The division among the electorate suggests that the outcome is in the hands of independents.

“Even though this really does appear to be, in a lot of ways, a rerun” of the first race between Walker and Barrett, “what has happened is that Walker and Barrett’s support hasn’t realigned in any way but things have simply polarized,” says Mr. McAdams.

Barrett won the primary with 58 percent of the vote to Falk's 34 percent. Secretary of State Doug La Follette received 4 percent, followed by state Sen. Kathleen Vinehout with 3 percent. Gladys Huber received less than 1 percent.